On coherent rotation angles for as-rigid-as-possible shape interpolation

The goal of morphing algorithms is to construct visually pleasing interpolations between 2D or 3D shapes, referred to as morphs in computer graphics circles. One of the desirable properties of morphing algorithms is avoiding self-intersections of the deforming shape. This paper investigates winding number-based topological invariants of planar morphs between compatible triangulations that do allow global self-intersections but avoid local ones. Equivalently, such morphs are not allowed to make any of the triangles degenerate. We show a relationship between those invariants and the as-rigid-as-possible shape interpolation algorithm and improve it so that it allows to handle cases when a large amount of twist is required to transform the source triangulation into the target triangulation.